Of 41 bank customers depositing a check, 15 received some cash back. (a) Construct a 90 percent confidence interval for the proportion of all depositors who ask for cash back. (Round your answers to 4 decimal places.) The 90% confidence interval is from (b) May normality of p be assumed? O Yes O No

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**Title: Confidence Intervals and Normality in Statistical Analysis**

**Problem Overview:**

Out of 41 bank customers depositing a check, 15 received some cash back.

---

**Questions:**

**(a)** Construct a 90 percent confidence interval for the proportion of all depositors who ask for cash back.  
*(Round your answers to 4 decimal places.)*

The 90% confidence interval is from [____] to [____].

**(b)** May normality of \( p \) be assumed?

- [ ] Yes  
- [ ] No  

---

**Explanation:**

This exercise involves calculating a confidence interval for a proportion. A confidence interval gives an estimated range of values which is likely to include an unknown population parameter, in this case, the proportion of depositors asking for cash back. Calculating this involves understanding the normality assumption, which generally requires the sample size to be sufficiently large for the Central Limit Theorem to apply.

The selection on whether normality can be assumed helps determine if the sample size is adequate to use the confidence interval methodologies that rely on this assumption.
Transcribed Image Text:**Title: Confidence Intervals and Normality in Statistical Analysis** **Problem Overview:** Out of 41 bank customers depositing a check, 15 received some cash back. --- **Questions:** **(a)** Construct a 90 percent confidence interval for the proportion of all depositors who ask for cash back. *(Round your answers to 4 decimal places.)* The 90% confidence interval is from [____] to [____]. **(b)** May normality of \( p \) be assumed? - [ ] Yes - [ ] No --- **Explanation:** This exercise involves calculating a confidence interval for a proportion. A confidence interval gives an estimated range of values which is likely to include an unknown population parameter, in this case, the proportion of depositors asking for cash back. Calculating this involves understanding the normality assumption, which generally requires the sample size to be sufficiently large for the Central Limit Theorem to apply. The selection on whether normality can be assumed helps determine if the sample size is adequate to use the confidence interval methodologies that rely on this assumption.
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